The area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides

C

AB = BC = CA =

∠ABC = ∠BCA = ∠CAB = Total =

AB² = BC² + CA², = +

As may you have noticed the blue square area equals the sum of the red square area and the green square area

Start dragging the points A,B to see how the areas affected.

Also check the rearrangment proof animation to help you understand it.

A2

B2

C2

+ =

Some of real life applications to the theorem

To calculate the length of staircase required to reach a window
To find the length of the longest item can be kept in your room.
To find the steepness of the hills or mountains.
To find the original height of a tree broken due to heavy rain and lying on itself.
To determine heights and measurements in the construction sites.